Critical speeds and critical axial loads of overhung shaft-disk systems

A lumped mass model is proposed to study the critical speeds and critical axial loads of the overhung shaft-disk systems. In the present study, both the exact and approximate stiffness influence coefficients of the axially loaded overhung shafts are derived. In order to obtain deeper insight into the dynamic behavior of such shaft-disk systems, the present shaft mathematical model has taken account of shear deformation effect. Because the exact stiffness influence coefficients of the system are highly transcendental and hard to get their characteristics on axial load intuitively, each stiffness influence coefficient is expanded in a Taylor's series about axial load. The elegant approximations of them are then obtained. Based on the present approximate stiffness influence coefficients, the critical speeds and critical axial loads of the overhung shaft-disk systems can be easily and quickly obtained. Numerical simulations show that the present results are seen to be quite in agreement with the exact solutions.